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[Masaki Akaogi](https://orcid.org/0000-0001-5259-8794), Takayuki Ishii, [Kazunari Yamaura](https://orcid.org/0000-0003-0390-8244)

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[Post-spinel-type AB2O4 high-pressure phases in geochemistry and materials science](https://mdr.nims.go.jp/datasets/e5509419-c031-49e6-82df-0c853e237621)

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Post-spinel-type AB2O4 high-pressure phases in geochemistry and materials sciencecommunications chemistry Review articlehttps://doi.org/10.1038/s42004-024-01278-0Post-spinel-type AB2O4 high-pressurephases in geochemistry and materialsscienceCheck for updatesMasaki Akaogi 1,2 , Takayuki Ishii3 & Kazunari Yamaura 4Post-spinel-type AB2O4 compounds are stable at higher pressures than spinel phases. Thesecompounds have garnered much interest in geo- and materials science for their geochemicalimportance as well as potential application as high ionic conductors and materials with stronglycorrelated electrons. Here, large-volume high-pressure syntheses, structural features and propertiesof post-spinels are reviewed. Prospects are discussed for future searches for post-spinel-type phasesby applying advanced large-volume high-pressure technology.Spinel-structuredAB2O4 compounds are of great interest in geoscience andmaterials science. The name “spinel” is derived from the mineral name,MgAl2O4 spinel. The spinel-type structure of AB2O4 consists of almostcubic-closed packing array of O2− with interstitial 4- and 6-fold coordina-tion sites in which A and B cations are accommodated. Most of spinel-typeAB2O4 compounds have cubic symmetry, and their physical properties areequivalent along the three axes.Whena spinel-typeAB2O4 compound is compressedunderpressure athigh temperature or at room temperature in some compounds, it trans-forms to a high-pressure phase or dissociates into an assemblage ofdecomposed phases, and these changes are associatedwith density increasesfrom the spinel-type phase. An AB2O4 compound stable at higher pressurethan the spinel-type is called a “post-spinel”phase. CaFe2O4-, CaTi2O4- andCaMn2O4-type structures with orthorhombic symmetry are well known asmajor post-spinel structures1. Hereafter, we abbreviate the CaFe2O4-,CaTi2O4- and CaMn2O4-types as CF-, CT- and CM-types, respectively. Incontrast to the spinel-type structure, all theCF, CT- andCM-type structuresin AB2O4 are composed of one-dimensional framework of BO6 octahedrawith A cations in 6- to 8-fold coordination sites2–6. These post-spinel-typephases are generally ∼10% denser than the corresponding spinel phases.The structural details are discussed later.We note that in solid Earth science the transformation of Mg2SiO4ringwoodite, a typical spinel-type A2BO4 compound, which occurs at∼660 km depth in the Earth’s mantle, is also named as the post-spineltransition7. The AB2O4 post-spinel phase is used as a term in both ofgeoscience and materials science.In geoscience, it is widely accepted that oceanic lithospheres coveredwith oceanic crust which consist of the top of the solid Earth are subductedinto the deepmantle. Sedimentary rocks on the oceanic lithospheres are alsosubducted together. Hereafter, the oceanic crust and sedimentary rocks arecalled as “crustal materials”. Chemical compositions of the oceanic crust8and sedimentary rocks9 are rich in SiO2, Al2O3, Na2O and K2O, comparedwith the average mantle composition10. By the subduction of the oceaniclithospheres, pressure-induced phase transitions of constituent minerals ofthe crustal materials take place at high-pressure and high-temperatureconditions in the Earth’s interior.To examine the phase transitions in the subducted crustal materials,phase relations of various silicate-aluminate systems and natural crustalmaterials have been investigated by high-pressure and high-temperatureexperiments. These studies have clarified that the CF-type phase is one ofmajor high-pressure minerals in the subducted crustal materials11–19. A“NAL” (New ALuminous) phase which has approximately 2/3AB2O4·1/3CB2O4 composition and hexagonal symmetry is another major high-pressure phase in the crustal materials16,20. In the following, we include theNAL-type phase into the group of post-spinel phases. This is because,similarly to the CF-, CT- and CM-type structures, the NAL-type structureconsists of one-dimensional arrays ofBO6octahedrawith 6- and 9-fold sitesfor A and C cations21. The structural characteristics of the CF-, CT-, CM-and NAL-type phases are accompanied with their interesting properties, asdescribed below.In this review, we first discuss recent developments in high-pressureand high-temperature experimental techniques, using large-volume high-pressure apparatus. Then, a variety of post-spinel-type oxide materials aretabulated, and crystal structural characteristics of the post-spinel-typecompounds are discussed in terms of ionic radii of constituent cations. Wedescribe some results on phase relations and properties on post-spinelphases of geochemical and mineralogical interest. Following this, the dis-cussion shifts to the perspective of materials science, highlighting theimportance of post-spinel-type compounds as highly ionic conductingmaterials and for their strongly correlated electronic properties.1Department of Chemistry, Gakushuin University, Toshima-ku, Tokyo, Japan. 2Geochemical Research Center, Graduate School of Science, The University ofTokyo, Bunkyo-ku, Tokyo, Japan. 3Institute for Planetary Materials, Okayama University, Misasa, Tottori, Japan. 4Research Center for Materials Nanoarchitec-tonics (MANA), National Institute for Materials Science, Tsukuba, Ibaraki, Japan. e-mail: masaki.akaogi@gakushuin.ac.jpCommunications Chemistry |           (2024) 7:189 11234567890():,;1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s42004-024-01278-0&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s42004-024-01278-0&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s42004-024-01278-0&domain=pdfhttp://orcid.org/0000-0001-5259-8794http://orcid.org/0000-0001-5259-8794http://orcid.org/0000-0001-5259-8794http://orcid.org/0000-0001-5259-8794http://orcid.org/0000-0001-5259-8794http://orcid.org/0000-0003-0390-8244http://orcid.org/0000-0003-0390-8244http://orcid.org/0000-0003-0390-8244http://orcid.org/0000-0003-0390-8244http://orcid.org/0000-0003-0390-8244mailto:masaki.akaogi@gakushuin.ac.jpwww.nature.com/commschemRecent developments in high-pressure andhigh-temperature experimental techniques usinglarge-volume apparatusIn solid Earth science, high-pressure and high-temperature experiments areindispensable to simulate P, T conditions of the Earth’s interior in labora-tories, and in materials science they are valuable to synthesize novel mate-rials which cannot be formed at atmospheric pressure. In these researchfields, large-volume high-pressure apparatus such as a cubic anvil-typeapparatus and a Kawai-type double-staged multi-anvil press are widelyused. The name “large-volume apparatus” is derived from comparisonwithrelatively small volume apparatus, particularly a diamond anvil cell (DAC).Although the laser-heated DAC enables to generate pressure more than300 GPa and temperature higher than 5000 °C, the sample weight of theDAC experiment is less than order of 1 μg22. The large-volume high-pres-sure apparatusmake it possible to synthesize a sample ofmore than 103–107times larger volume than that available by the DAC in the samepressure range.Figure 1 illustrates the cubic anvil press and Kawai-type multi-anvilapparatus together with their typical cell assemblies. In the cubic anvil press,a pressure-medium cube is compressed by six anvils. In the Kawai-typemulti-anvil apparatus, six 1st-stage (outer) anvils compress eight 2nd-stage(inner) anvils. The eight inner anvilswhose corner is truncated into a regulartriangular face compress an octahedral pressure-medium. Generally, thecubic anvil press is used up to ∼10GPa, and the Kawai-type multi-anvilpress up to∼25 GPa, to synthesize a large amount of polycrystalline samplein a single experimental run at high pressure and high temperature. In thecubic anvil press and Kawai-type multi-anvil apparatus, samples of severalten grams can be synthesized at pressures up to∼5–10 GPa, and those of upto several ten milligrams by using the Kawai-type apparatus at ∼25GPa athigh temperature conditions. More details are given in the literature23,24.The large-volume presses have several other advantages: the precisecontrol of pressure and temperature and the relatively uniform temperaturedistribution in the sample chamber using a furnace inside the pressuremedium. Generally, in the experiments using the large-volume apparatus, astarting material is charged in a noble metal capsule such as Pt, Au and Re,which is placed in the central part of pressuremedium. The capsulewith thesample in the pressuremedium isfirst compressed at room temperature to adesired pressure, and then temperature is elevated by supplying electricpower to the heater. After being kept at the P, T condition for a certainperiod, e.g., several minutes to several hours depending of temperature, thesample is quenched under pressure by shutting off the heating power, and isrecovered after release of pressure. This experimental procedure is called thesample-quenching method, allowing us to recover a high-pressure phasekeeping its crystal structure under high pressure and high temperature.Fig. 1 | High-pressure experimental techniques using the large-volume appara-tus. (a, b) the cubic multi-anvil press and the typical cell assembly. (c, d) the Kawai-type multi-anvil press and the cell assembly. The cubic multi-anvil press is generallyused for experiments up to about 10 GPa. The DIA-type guide block in (a) is alsocalled the Osugi-type47. The Kawai-type multi-anvil press is applied for experimentsgenerally up to about 25 GPa. The cubic multi-anvil press can be scaled up andcombined with the Kawai-type cell assembly to generate pressures up to 65 GPa. Athermocouple, not shown in (b) and (d), is inserted into each of the cell assemblies tomonitor the sample temperature.https://doi.org/10.1038/s42004-024-01278-0 Review articleCommunications Chemistry |           (2024) 7:189 2www.nature.com/commschemSingle-phase materials with large quantities such as several tens ofmilligrams to several tens of grams synthesized at high pressure and hightemperature are usually needed for accuratemeasurements of their physicaland chemical properties. For example, thermodynamic properties(enthalpies, entropies and heat capacities) of high-pressure silicates whichare stable in the Earth’s interior have been measured at ambient pressure,using the quenched samples of several tens of milligrams to severalgrams25–31. Polycrystalline superhard materials have been synthesized usingthe multi-anvil techniques, such as nano-polycrystalline diamond withseveral gram quantity32,33.By using the large-volume apparatus, synthesis of single-crystals ofseveral tens to hundreds μm in size is easily made in a pressure range up to∼25 GPa, and are recovered at ambient conditions34,35. These large single-crystals canbeused for single-crystalX-raydiffraction structure analysis andspectroscopic measurements. Especially, combination of such a single-crystal with DAC techniques have contributed to significant progress oncharacterization of geomaterials at high pressure by measurements such asBrillouin scattering, Raman, and Mössbauer spectroscopies36,37.Control of fugacities of oxygen, water, etc., in the sample chamber canbemade in the experiments using the large-volume apparatus. For example,oxygen fugacity is controlled by using oxygen buffers such as Fe-FeO andRe-ReO2 or by adding oxidizing agents such as KClO3, KClO4 and NaClO3which release oxygen at high temperature. These methods allow us tosynthesize single- or mixed-valence cation (Fe2+ and/or Fe3+)-bearingcompounds and abnormal valence cation (e.g., Fe4+)-bearingcompounds38–40. Also, single-crystals of a high-pressure phase with up toseveralmm in size can bemade bymixing an appropriate flux such as waterand NaCl with the starting material41–43. The combination of large-volumeapparatus with synchrotronX-ray radiation is a powerfulmethod for in situobservation of structural changes of the sample44,45. The details of the in situX-ray observation method are found in the literature23.In the experiments of the Kawai-type double-staged multi-anvilapparatus, tungsten carbide (WC) anvils are usually adopted for the second-stage anvils. Before the 2000s, generatedpressurewas limited up to∼25 GPaat temperature of ∼1000–2000 °C, using the Kawai-type multi-anvil appa-ratus. Recently, the pressure limit was extended to ∼65 GPa at room tem-perature and ∼50 GPa at temperature up to ∼1700 °C by using newlyinvented hardened WC anvils with effective control of pressure and tem-perature generation efficiencies46,47. Samples with half milligrams and~50–100 μm-sized single-crystals have been synthesized, allowing to per-form crystal structure analysis and optical measurements under pressure ina DAC48,49. This expansion of pressure provides new opportunities forstudies on phase transitions and physical properties of the materials in thedeep part of the Earth’s mantle and for synthesis of a wider range of novelmaterials.Crystal structures of post-spinel phasesCaFe2O4-, CaTi2O4- and CaMn2O4-type phasesTable 1 summarizes post-spinel-structured AB2O4 high-pressure phases ofEarth’s minerals studied in geoscience, and also some post-spinel-typeminerals stable at atmospheric pressure. Table 2 lists post-spinel-typeAB2O4 phases synthesized at atmospheric and high pressure from theinterest of materials science.CaFe2O4 (CF)-, CaTi2O4 (CT)- and CaMn2O4 (CM)-type structures,all of which are orthorhombic in symmetry, are the post-spinel structuresfor various AB2O4 compounds. Figure 2a, b illustrates the CF-type (Pnma)andCT-type (Cmcm) structures, respectively, where symbols in parenthesesrepresent space groups. Both of the structures consist of double chains ofedge-sharingBO6 octahedra, which contain 6-fold coordinatedB cations byO2−. The double chains are running parallel to one of the orthorhombic cellaxes. Four double chains form a tunnel-like space by corner-sharing of BO6octahedra. In the tunnel spaces, A cations are accommodated in 8-foldcoordinated bicapped prism sites (for the CT-type, see more details below).Although the two structures in Fig. 2a, b look very similar, arrangements ofthe double chains of octahedra are different between CF- and CT-typestructures, as shown by the difference in space group. The CaMn2O4 (CM)-type structure (Pbcm) is essentially the same as CT-type in the arrangementof octahedra, but it is different fromCT-type because octahedra of the CM-type structure are distorted by Jahn-Teller active ions such as Mn3+ (3d4)6.Due to the distortion, the space group of CM-type is lower than that ofCT-type.When we look at the CF- and CT-type structures in more detail, thecoordination environments ofA cations in both the structures are different.Structure analysis of CF-typeMgAl2O450 indicated that eightA-O distancesin the 8-fold coordinated bicapped prism sites spread over a wide range,2.13–2.49 Å. However, in the CT-structured MgAl2O449, eight A-O dis-tances are divided into two groups; two longA-Odistances of 2.56 Å and sixshort ones of 2.02–2.21 Å. The latter six A-O bonds form a trigonal prismsite. Therefore, A cations in the CT-type is regarded as practically in the6-fold trigonal prism sites rather than the 8-fold sites. These structuraldifferences imply that the CF-type structure is more flexible to accom-modate cations of a wider range in size, compared with those in the CT-type51. The differences are also reasons thatCF-type phase forms at awide P,T range in the Earth’s deep interior of multi-component systems, asdescribed in section “Post-spinel phases in geochemical and mineralogicalinterest”, and that CT-type phase does not frequently appear even incompositionally simple systems.NAL-type phaseIn some binary AB2O4-CB2O4 systems, a high-pressure phase with anintermediate composition, 2/3AB2O4·1/3CB2O4 or A2CB6O12, is stable andhas a structure with hexagonal symmetry. ThisA2CB6O12 phase is the NALphase (P63/m), and its structure is shown in Fig. 2c21. The structural fra-mework of the A2CB6O12 phase is double chains of edge-sharing BO6octahedra running parallel to the c-axis, like CF-, CT- and CM-types. TheNAL phase structure, however, has three different sites for cations. They aresmall octahedral sites forB,middle-sized6-fold trigonal sites forA, and large9-fold sites forC. As shown in Fig. 2c, the 9-fold and 6-fold trigonal sites areformed in tunnel spaces surrounded by the double chains of octahedra. Theoccupancy of the 9-fold sites is 0.50 in the A2CB6O12 composition.Post-spinel phases in geochemical and mineralogicalinterestExperimental studies on phase transitions of various spinel-type AB2O4compounds at high pressure and high temperature have indicated severaldifferent pathways from spinel-type to post-spinel-type. Thefirst one is thata spinel-type AB2O4 directly transforms to a post-spinel-type phase. Forexample, spinel-typeMnCr2O4 transforms to CF-type phase at∼10 GPa at1000–1200 °C51. Other types are that a spinel-type AB2O4 first dissociatesinto two phases, which then combine into a singleAB2O4 post-spinel phaseat higher pressure. Three kinds of the dissociated phase assemblages havebeen reported so far; rock-salt (Rs)-type AO+ corundum (Cor)-type B2O3(e.g., MgAl2O4, FeV2O4), modified-ludwigite (mLd)-type A2B2O5 + Cor-typeB2O3 (e.g.,MgAl2O4, FeCr2O4), andCaFe3O5-typeA2B2O5+Cor-typeB2O3 (e.g., Fe2+Fe3+2O4)52–55.In geoscience, precise phase relations of geomaterials at high pressureandhigh temperature are essential to apply the results to the Earth’s interior.The large-volume high-pressure techniques are necessary to obtain theaccurate phase relations, because of precise control of pressure and tem-perature, compared particularly with the DAC experiments. In the fol-lowing, we show, as examples, high-pressure and high-temperature phaserelations in MgAl2O4 and those in the CaAl2O4-MgAl2O4 system (Fig. 3)determined by the large-volume presses.Figure 3a exhibits the phase relations in MgAl2O4 up to ∼35 GPa and∼2700 °C, based on the experimental data by the large-volumeapparatus49,53,56–58. Below ∼2000 °C, spinel-type MgAl2O4 dissociates intoRs-typeMgO+Al2O3 Cor at∼15–18 GPa, and they combine into CF-typeat ∼27 GPa. Above ∼2000 °C, however, spinel decomposes into mLd-type+ Cor at ∼20–22 GPa, which combine into CF-type MgAl2O4 phase at∼26 GPa. The CF-type phase further transforms to CT-type at aroundhttps://doi.org/10.1038/s42004-024-01278-0 Review articleCommunications Chemistry |           (2024) 7:189 3www.nature.com/commschem30–35 GPa49,59–61. Although the transition boundary between CF- and CT-phases has not yet been fully constrained, the CT-type has been synthesizedat 27 GPa and 2500 °C49 and at 50 GPa and 1700 °C61.We note that the firststructure analysis of CT-type MgAl2O4 was made using a single-crystal of∼40 μm in size synthesized at 45 GPa and∼1700 °C by the advancedmulti-anvil techniques49. Recovered MgAl2O4 samples from the region of∼26–30 GPa above ∼2200–2500 °C have a novel structure different fromCF- and CT-types49,53, which will be discussed later.Some AB2O4 phases which do not have the spinel structure at atmo-spheric pressure transform to post-spinel-type phases at high pressure.CaAl2O4 andNaAlSiO4 have the stuffed-tridymite structure at atmosphericpressure, and both the phases transform to CF-type at ∼10 and ∼20 GPa,respectively, at 1200 °C via some intermediate phases57,62.Phase transitions amongCF-, CM- andCT-type phases have also beenobserved. In FeCr2O4, a spinel-type phase decomposes at ∼18 GPa and1300 °C into mLd + Cor, and they combine into CF-type, which furthertransforms to CT-type at ∼28 GPa54. We note that the high-pressureFeCr2O4 polymorphs and mLd-type Fe2Cr2O5 were successfully synthe-sized under controlled oxygen fugacity with the Fe-FeO buffer in themulti-anvil experiments described in section “Recent developments in high-pressure and high-temperature experimental techniques using large-volume apparatus”. The CF-type FeCr2O4 is not quenchable but changesduring decompression into a new, modified CF-type phase with a five-foldcoordination for A-site cations in the tunnel space. By room temperaturecompression, CM-type CaMn2O4 transforms discontinuously at ∼30 GPato CT-type, which is not quenchable and back-transforms to the CM-typeon release of pressure6, indicating that the Jahn-Teller distortion of MnO6octahedra is suppressed at high-pressure conditions in the CT-type phase.New-structured post-spinel phases were recently discovered inMgAl2O4 and MgFe2O4 as recovered samples from 20–27 GPa and1200–2500 °C49,63. They have B-site polyhedral frameworks and tunnelstructureswhich are different from those of theCF-, CT, andCM-types, It isexpected that further new-structured post-spinel phases can be discoveredby applying the advanced high-pressure technology.Figure 3b shows a schematic diagram of phase relations in theCaAl2O4-MgAl2O4 system up to 32 GPa at 1200 °C57,64. CaAl2O4 andMgAl2O4 transform to CF-type at ∼8 and ∼28 GPa, respectively57. In anTable 1 | Post-spinel-type high-pressure phases of Earth’smineralsPhase Structure Transition P,T Structure Ref.P(GPa) T (°C) analysisMgAl2O4 CF 27 1600 R 50,57MgAl2O4 CT 27 2500 SC 49MgCr2O4 CT 18 1400 R 99FeCr2O4 CFa 18 1300 P 54FeCr2O4 CT 28 1300 R 54NaAlSiO4 CF 19 1200 R 62,91CaAl2O4 CF 8 1200 R 57,100CaFe2O4 CF 0 1250 SC 2CaTi2O4 CT 0 1000 SC 5CaMn2O4 CM 0 1250 SC 3CaMn2O4 CTa 30 25 R 6Mn3O4-II CM 11 1000 R 101,102Mg2CaAl6O12 NAL 16 1200 R 21,64Mg2NaAl5SiO12 NAL 14 1500 R 65,66Mg2KAl5SiO12 NAL 16 1500 R 64,66These phases are stable in the Earth’s interior as endmembers of mineral solid solutions. CF:CaFe2O4-type, CT: CaTi2O4-type, CM: CaMn2O4-type, NAL: NAL-type, R: Rietveld structurerefinement, SC: single-crystal structure analysis, P: powder X-ray diffraction method.aUnquenchable phase at atmospheric pressure.Table 2 | Post-spinel-type phases synthesized at atmosphericpressure and at high pressure in the interest of materialssciencePhase Structure Synthesis P,T Structure Ref.P(GPa) T (°C) analysisCaV2O4 CF 0 1200 R 103Ca2/3Mn2O4 CF 0 1200 R 104SrTl2O4 CF 0 900 R 105SrLn2O4(Ln =Gd, Ho,Yb)CF 0 1500 R 106BaLn2O4 (Ln = La, Nd,Sm, Gd, Ho, Yb)CF 0 820–1000 SC 107LiVTiO4 CF 0 390 R 89LiCrTiO4 CF 0 450 R 89LiFeTiO4 CF 0 350 R 108LiRhTiO4 CF 0 450 R 89LiMn(Sn1-x,Tix)O4(x = 0, 0.3, 0.45)CF 0 350 R 89LiM0.5Ti1.5O4 (M =Mg,Co, Fe)CF 0 350–390 R 89NaTi2O4 CF 0 1200 SC 84NaRu2O4 CF 0 950 SC 94NaCrTiO4 CF 0 900 R 88NaRhTiO4 CF 0 950 R 88NaV1.25Ti0.75O4 CF 0 700 R 109NaCrSnO4 CF 0 1000 R 88NaMnSnO4 CF 0 1200 R 88NaInSnO4 CF 0 1200 R 88NaVSnO4 CF 0 750 R 109Na0.56Ti0.28Fe1.72O4 CF 0 1220 SC 110(A,Bi)2/3-xRh2O4 (A =REE)CF 0 1000 SC 111NaAlGeO4 CF 12 900 P 112MgMn2O4a CM 15 25 R 86MFe2O4a (M =Mg,Fe, Zn)CT 25-40 25 R 113MnCr2O4 CF 10 1200 R 51FeV2O4 CT 11 1200 R 51ZnGa2O4a CM 55 25 P 79CuRh2O4 CF 4 900 P 114CdRh2O4 CF 6 1400 R 115CdCr2O4 CF 10 1100 R 116CaCo2O4 CF 6 1500 R 117CaRh2O4 CF 6 1500 SC 96NaV2O4 CF 6 1700 SC 43NaMn2O4 CF 4.5 1100 SC 92NaRh2O4 CF 6 1500 R 96LiMn2O4 CF 6 1200 R 82NaLi2Ru6O12 NAL 0 1100 SC 90KLi2Ru6O12 NAL 0 1100 SC 90SrBe2Rh6O12 NAL 0 1000 P 93SrMg2Rh6O12 NAL 0 1000 P 93REE rare earth element.These phases synthesized in laboratories are not present in the Earth’s interior. CF: CaFe2O4-type,CT: CaTi2O4-type, CM: CaMn2O4-type, NAL: NAL-type, R: Rietveld structure refinement, SC:single-crystal structure analysis, P: powder X-ray diffraction method.aUnquenchable phase at atmospheric pressure.https://doi.org/10.1038/s42004-024-01278-0 Review articleCommunications Chemistry |           (2024) 7:189 4www.nature.com/commschemapproximate composition of 1/3CaAl2O4·2/3MgAl2O4 or CaMg2Al6O12, aNAL-type phase with the compositional width of ∼5mol % is stable in thesystem above∼16 GPa. In the NaAlSiO4-MgAl2O4 and KAlSiO4-MgAl2O4systems, NAL-type phases are stable above ∼15 GPa at 1200–1600 °C in awide compositional range up to∼20mol %64,65. Composition analysis65 andstructure analysis66 of the NAL phase solid solutions in the NaAlSiO4-MgAl2O4 system revealed that the occupancy in the 9-fold sites deviatedfrom 0.50 to ∼0.45. Tables 1 and 2 include the various NAL-type phases.As described in Introduction, post-spinel-type phases of aluminoussilicate compositions are stable in the Earth’s lower mantle conditions. Inaddition to the simplified silicate-aluminate systems discussed above, anumber of high-pressure and high-temperature experimental studies onnatural crustal compositions indicated that CF- and NAL-type phasesbecome stable as major aluminous phases in the lower mantleconditions11–13,15–18,67,68. In particular, the CF-type phase is stable in thepressure range of∼24–135 GPa in the whole lower mantle (∼660–2900 kmin depth). In the crustal materials in the lower mantle, NaAlSiO4 andMgAl2O4 are twomajor components in the CF-phase13,16–19. The NAL-typephase contains not only the two components but also KAlSiO4component64,66,67. In contrast, the other major minerals stable in the lowermantle conditions, i.e., Mg-rich bridgmanite with the orthorhombic-perovskite structure, rock-salt type (Mg, Fe)O ferropericlase, CaSiO3-richcubic-perovskite phase, and SiO2 stishovite, contain almost no Na+ and K+in the structures17,19,69.Among geochemically abundant elements of the solid Earth, Na+and K+ play important roles in melting and differentiation in theEarth’s interior. Therefore, subduction of crustal materials containingCF- and NAL-type phases into the lower mantle is one of mostimportant processes for circulation of materials including the alkalielements in the Earth’s interior70. In addition, host-phases of K+ inthe deep mantle are of significant importance in the Earth’s thermalhistory, because a long-lived radiogenic element 40K is a major heatsource in the Earth’s interior71. A K-rich NAL phase with theapproximate composition of KMg2Al5SiO12 is stable even at∼135 GPa and ∼2000 °C, which correspond almost to the Earth’score-mantle boundary conditions72. This result suggests that the NALphase may be a candidate of high-pressure minerals which transportK from the mantle into the core73.Physical properties of CF-, CT- (if exists) and NAL-type phases ingeochemical systems, such as electrical conductivity and rheology, mayprovide new insights for understanding of the structure anddynamics of theEarth’s interior. As will be discussed in section “Post-spinel phases inmaterials science”, the post-spinel phases in geochemical systems also areexpected to have potentially distinctive transport properties, because ofpossible high ionic conduction (fast cation diffusion) through and largethermal vibration of cations in the tunnel structures. Although transportproperties of dominant minerals in the mantle such as olivine and bridg-manite have been investigated74, no such studies have been reported on theFig. 2 | Crystal structures of post-spinel phases. (a) CaFe2O4(CF)-type, (b)CaTi2O4(CT)-type, and (c) NAL-type structures. In (a) and (b) of the post-spinelAB2O4 phases, the large brown spheres and small red spheres express A and O,respectively.Middle-sized blue spheres in the octahedra areB. In (c) of theNAL-typeA2CB6O12 phase, large blue/silver spheres and small red spheres represent C (halfoccupancy) and O, respectively. Brown spheres are A, while blue spheres in theoctahedra are B. Structure data: (a) CF-type MnCr2O451, (b) CT-type MgCr2O499,and (c) Mg2CaAl6O1221. Drawn with VESTA118.https://doi.org/10.1038/s42004-024-01278-0 Review articleCommunications Chemistry |           (2024) 7:189 5www.nature.com/commschempost-spinel phases in the geochemical systems. Therefore, these studied willbe paid more attention in solid Earth science in near future.Crystal chemical characteristics of post-spinel phasesin terms of cation radiiFigure 4a exhibits structure types of a variety of post-spinel A2+B3+2O4compounds synthesized at atmospheric and high pressure, in terms of8-fold coordinated A2+ radius, R(A2+), and 6-fold coordinated B3+ radius,R(B3+). We use Shannon’s ionic radii75 throughout this article. The data inFig. 4a, b are based on those summarized in Tables 1 and 2, in addition tothose from other literature shown in the figure caption. All the post-spinelphases in Fig. 4 are quenchable to ambient conditions.As shown in Fig. 4a, CF-type A2+B3+2O4 compounds with R(A2+) andR(B3+) smaller than∼1.1 and∼0.65 Å, respectively, can be synthesized onlyat high pressure. This is consistent with the ideas that radii of theseA2+ andB3+ ions are too small at atmospheric pressure to occupy the cation sitescoordinated byO2- anions in the post-spinel-typeA2+B3+2O4 structures, andthat relatively large O2- is more compressible than relatively small A2+ andB3+. In Fig. 4a, CM-type phases appear only in A2+Mn3+2O4 compounds,because of the Jahn-Teller active Mn3+ ions. The CM-type phases may beincluded in theCT-type group, as discussed in section “CaFe2O4-, CaTi2O4-and CaMn2O4-type phases”. Figure 4a shows that CF-type A2+B3+2O4phases are formed in wide ranges of A2+ and B3+ radii, ∼0.89–1.42Å and∼0.53–1.03Å, respectively. On the other hand, CT-and CM-type high-pressure phases are synthesized only in the region of R(A2+) smaller than∼0.95 Å. These characteristics can be explained by the structural differencebetween CF- and CT-types, i.e., A2+ cations in CF-type are accommodatedin the larger 8-fold coordinated bicapped-triangular prism sites, while thosein CT-type are in the smaller 6-fold triangular prism sites, as described insection “CaFe2O4-, CaTi2O4- and CaMn2O4-type phases”.Figure 4b shows the structure types of A+(B3+B’4+)2O4 compoundsin terms of R(A+) and the average of R(B3+) and R(B’4+), where A+ is an8-fold coordinated cation and B3+ and B’4+ are 6-fold ones. The figureexhibits that CF-type A+(B3+B’4+)2O4 compounds with R(A+) and 1/2(R(B3+)+ R(B’4+)) smaller than∼1.18 and∼0.62 Å, respectively, can besynthesized only at high pressure, though the data are limited. Thistendency is similar to that in Fig. 4a. In addition, the structures ofLiMn2O4, NaMn2O4 and NaMnSnO4 are not CM-type but CF-type.This indicates that the CF-type structure is formed, even when half of Bcations are Jahn-Teller active ions, further supporting the more flexiblestructure of CF-type than CT/CM-type.For a givenA2+B3+2O4 orA+(B3+B’4+)2O4 composition, the diagrams inFig. 4 can be used to predict whether the post-spinel-type phase can besynthesized at atmospheric pressure or is stable only at high pressure andwhich phase is stable between CF-type and CT-type (including CM-type).These may help us design new post-spinel phases with expected structureand properties. For example, it may be suggested from Fig. 4a that spinel-type ZnCr2O4 transforms to CT-type rather than CF-type at high pressure.Although stability of some post-spinel phases of AB2O4 have beenstudied by theoretical methods such as the density functional theory(DFT)76,77, such investigations are still limited.TheDFTstudies revealed thatMgAl2O4 spinel first dissociated at∼15 GPa intoMgO+Al2O3 corundum,which then combined into CT-type at∼45 GPa, though CF-type MgAl2O4and modified ludwigite-type Mg2Al2O5 were not taken into account in thecalculations (see Fig. 3a). A first-principles calculation study suggested thatspinel-type ZnGa2O4 transformed to CM-type at 39 GPa and spinel-typeZnAl2O4 to CF-type at 33 GPa78. The in situ X-ray diffraction experimentsshowed that CM-type of ZnGa2O4 occurs at ∼55 GPa79, though the post-spinel transition inZnAl2O4 has not yet been found experimentally. Furthertheoretical studies on post-spinel transitions in a variety of AB2O4 com-pounds are desirable to compare with previous experimental results andpredict future directions of experimental studies.Post-spinel phases in materials scienceIonic conductionPost-spinel AB2O4 phases are of significant interest not only in geosciencebut also inmaterials science.Theone-dimensional arrangement ofA cationsin the tunnel spaces of the post-spinel structures suggests the potential forionic conduction through the tunnels80,81. However, the extent of ionicmobility in these structures remains debated, necessitating further experi-mental investigations.Despite this uncertainty, some post-spinel-type AB2O4 compoundswith redox-active B cations have garnered attention as potential high-performance cathode materials for rechargeable batteries due to their pos-sible high cationic mobility. For instance, the spinel-to-CF transition inLiMn2O4 was first reported through high-pressure and high-temperaturesynthesis experiments82. The study showed that the polycrystalline samplesynthesized at 6 GPa and 900–1500 °C has a CF-type structure with thecomposition of Li0.92Mn2O4 and an activation energy barrier for ionicconduction approximately two-thirds that of spinel-type LiMn2O4, sug-gesting enhanced Li+ mobility after the spinel-to-CF transition. Furthersynthesis studies revealed that stoichiometric CF-type LiMn2O4 could notbe synthesized at 6 GPa and 600–1000 °C, with coexisting decompositionproducts such as Li2MnO3 affecting the rechargeable capacity83. Thesefindings underscore the complexity and need for continued research to fullyunderstand the ionic mobility and practical applications of post-spinelmaterials.Recent studies have also synthesized CF-structured NaMn2O4 at4.5 GPa and 1100 °C84, demonstrating stable battery performance duringNa+ ion insertion and extraction85. Similarly, MgMn2O4 has shown atransition to a CM-type phase at 15 GPa at room temperature due to theJahn–Teller distortion of Mn3+O6 octahedra86. Further studies on the CM-type MgMn2O4 concerning its ionic mobility are anticipated.First-principles calculations indicate that CF-type AMn2O4 (A = Li,Na,Mg) compoundshave lowerenergybarriers for thediffusionof Li+,Na+,and Mg2+ in tunnel spaces, compared to their CT- and CM-typeFig. 3 | High-pressure and high-temperaturephase relations of some typical post-spinel phases.(a)MgAl2O4, and (b) the CaAl2O4-MgAl2O4 systemat 1200 °C. In (a), Sp: MgAl2O4 spinel, Rs: rock-salt-type MgO, Cor: Al2O3 corundum, mLd: modifiedludwigite-type Mg2Al2O5, CF: CaFe2O4-typeMgAl2O4, CT: CaTi2O4-type MgAl2O4. In (b),Ca-CF: Ca-rich CaFe2O4-type solid solution,Mg-CF: CaFe2O4-type MgAl2O4, NAL: NAL-typesolid solution.https://doi.org/10.1038/s42004-024-01278-0 Review articleCommunications Chemistry |           (2024) 7:189 6www.nature.com/commschemcounterparts87, aligning with the structural flexibility of CF-type phases, asdiscussed in Section 3.At atmospheric pressure and high temperature, several Na-bearingpost-spinel compounds with the CF-type structure were recently synthe-sized, e.g., NaB3+TiO4 (B =Cr, Rh), NaB3+SnO4 (B =Mn, Cr, In), andrelated solid solutions88. The results significantly expanded the composi-tional space of Na-bearing CF-type phases synthesized at atmosphericpressure, providing helpful insights for searching potential battery electrodematerials. Furthermore, several Li-containing post-spinel compounds withthe CF-type structure were synthesized very recently at atmospheric pres-sure and high temperature from Na-bearing post-spinel counterparts byLi+-Na+ exchange process, e.g., LiB3+TiO4 (B =V,Cr, Rh) and LiMnSnO489.The results suggest that the Li-post-spinel compounds may be promisingcandidates for newLi-ion energy storagematerials. High-pressure synthesismethods may expand the compositional space further and deepen ourunderstanding.NAL-type phases are also of interest in materials science. As shown inFig. 2c, the NAL-type structure has three different sites for cations: small6-fold octahedral sites, middle 6-fold trigonal sites, and large 9-fold sites.TheNAL-type phases have been synthesized not only in aluminous silicatesdescribed in section “NAL-type phase” but also in other compositions suchas platinum-group metal oxides. Several ruthenium oxides, ALi2Ru6O12(A =Na, K, Ca, Sr), were synthesized at atmospheric pressure at 1100 °C,and the structure analysis indicated thatKLi2Ru6O12 andNaLi2Ru6O12havethe NAL-type structure90. In these phases, Ru and Li are placed in theoctahedral and middle-sized 6-fold trigonal sites, respectively, while K andNa occupy the large 9-fold sites. Na+ is incorporated in the large 9-foldcoordination site of the NAL-type structure in both aluminous silicates andruthenium oxides. Structure analysis of NAL-typeNa1.04Mg1.88Al4.64Si1.32O12 indicated that the average Na-O distance inthe 9-fold site is 2.64 Å66, while those in the 8-fold sites in the CF-typeNaAlSiO4 and NaMn2O4 are 2.40 and 2.44 Å, respectively91,92. The large9-fold sites in the tunnel spaces of theNAL structuremay suggest potentiallyhigh Na+ mobility in the structure.Rhodium oxides AA’Rh6O12 (A = Sr, La, Bi, Pb; A’ =Mg, Li, Be) withthe NAL-type structure were also synthesized at atmospheric pressure at1000–1100 °C. Their electrical and magnetic properties showed high elec-trical conductivity and a high Seebeck coefficient, suggesting they could bepromising candidates for thermoelectricmaterials at high temperatures93, aswill be mentioned in the next section. High-pressure studies on theexploration of new NAL-type phases have not been active in materialsscience, but it is hoped that exploratory studies will progress. For example,expansion of the compositional range by using high-pressuremethodsmayimprove thermoelectric performance.Fig. 4 | Crystal structure types of post-spinelphases in terms of cation radii. (a) A2+B3+2O4 and(b) A+(B3+B’4+)2O4 synthesized at atmosphericpressure (open symbols) and at high pressure(closed, blue and red symbols). Circles, squares andtriangles: CaFe2O4(CF)−, CaTi2O4(CT)− andCaMn2O4(CM)-type phases, respectively. R(Mn+) inthe vertical axes express cation radii ofMn+ in 8-foldcoordination, and those in the horizontal axesrepresent those in the 6-fold coordination75. Data arefrom Tables 1 and 2 and from the literature forMgSc2O4119, CaCr2O4120, CaSc2O4121, CaLu2O4122,CaYb2O4122 and SrSc2O4123.https://doi.org/10.1038/s42004-024-01278-0 Review articleCommunications Chemistry |           (2024) 7:189 7www.nature.com/commschemStrongly correlated propertiesRecent advances inmulti-anvil high-pressure experimental techniques havesignificantly advanced materials science. As discussed in section “Recentdevelopments in high-pressure and high-temperature experimental tech-niques using large-volume apparatus”, the large capacity of high-pressuresynthesis technology has facilitated precise structural analysis and evalua-tion of strongly correlated physical properties through measurements suchas electronic transport, magnetic properties, and thermal properties mea-surements, especially neutron scattering experiments that usually requiresample masses in the order of several grams. The contribution of theseadvanced measurement technologies and the capacity to produce largehigh-pressure synthetic samples is noteworthy.Research on large sample masses of post-spinel-type oxides synthe-sized under high-pressure conditions has highlighted their potential asmaterials with strongly correlated electronic properties. A particular focushas been on oxides exhibiting metallic conductivity, such as NaRu2O494.Synthesized in 2006, NaRu2O4 is recognized as an unusual post-spinel-typeoxidewithmetallic conductivity95. Recent studies have unveiled a significantcorrelation between dimerization and charge ordering, facilitated by theformation of metal-metal bonds94. Similarly, NaRh2O4, synthesized in 2005as the first metallically conducting post-spinel oxide, has attracted con-siderable attention96. Theoretical calculations suggested that substituting Cafor Na in the post-spinel-type NaRh2O4 could significantly enhance itsthermoelectric properties, targeting a ZT of approximately 0.79 at 250 K97.Here, the figure of merit ZT, which quantifies the efficiency of a material’sthermoelectric power conversion, is defined as ZT = S2σT/κ, where S is theSeebeck coefficient, σ is the electrical conductivity, T is the absolute tem-perature, and κ is the thermal conductivity.However, initial experimentsdidnot confirm these anticipated improvements96, highlighting the need forfurther investigation into their potential as thermoelectric materials.Post-spinel-type NaV2O4, first synthesized in 2007 with the fluxgrowthmethod by large-volume high-pressure experiments, exhibits a half-metallic ground state43, andwas recently proposed as amagnetic topologicalmaterial98, making it promising for spintronic applications. The growth ofhigh-quality single crystals under highpressure, utilizing large sample space,is crucial for further investigation of these properties.Conclusions and outlookHigh-pressure and high-temperature experimental techniques using thelarge-volume apparatus have been extensively developed in the last twodecades. In a single experimental run by the large-volume press, a high-pressure phase of several ten grams can be synthesized at pressures up to∼10 GPa and several ten milligrams up to ∼25 GPa under controlledatmosphere. Furthermore, a sample of approximately half milligram hasbeen able to synthesize at pressures up to ∼50GPa, as described in section“Recent developments inhigh-pressure andhigh-temperature experimentaltechniques”. Single-crystals large enough for structure analysis and spec-troscopic studies can be synthesized in the whole pressure range shownabove. These advancements in high-pressure and high-temperature tech-nologyhave significantly impactedboth geoscience andmaterials science. Inrecent decades, various new AB2O4 post-spinel phases have been synthe-sized at high-pressure and high-temperature conditions, and the structureshave been analyzed and their physical and chemical properties have beenmeasured. This review article summarized progress of the research on thesepost-spinel-type compounds in geoscience and materials science.The crystal structures of CF-, CT- and CM-type AB2O4 post-spinelphases are composedwithone-dimensional double chains ofBO6octahedraand A cation arrays in tunnel spaces surrounded by the octahedral chains.The CM-type structure is essentially the same as the CT-type except fordistortion of the BO6 octahedra. CF-type AB2O4 phases crystallize in wideranges of ionic radii ofA2+ andB3+, whileCT-typephases crystallize inmuchnarrower cation radius ranges. This fact is consistent with the difference ofthe tunnel structures, i.e., the A2+ site of CF-type is geometrically moreflexible than that of CT-type. The relationship between the structure-typeand A2+ and B3+ radii can be used to predict which phase is stable at highpressure. Similarly to the CF-, CT- and CM-types, NAL-type 2/3AB2O4·1/3CB2O4 phases have the structure consisting of one-dimensional chains ofBO6 octahedrawith two kinds of tunnel spaces inwhichA andC cations areaccommodated, respectively, in 6- and 9-fold sites.In geochemical point of view, stability and phase relations of CF-, CT-and NAL-type phases in simple aluminate-silicate systems and in naturalcrustal compositions have been precisely determined up to∼ 25 GPa by thelarge-volume multi-anvil experiments. It has been clarified that the CF-phase accommodates Na+ in the structures, while the NAL-phase incor-porates both of Na+ and K+. Because investigations on the precise phaserelations above∼25 GPa are quite limited, detailed studies are necessary atpressure up to at least∼50 GPa to clarify the roles of Na+ and K+ in theEarth’s deep mantle. In addition, investigations on transport properties ofCF-, CT- and NAL-type phases in the geochemical systems will beimportant for understanding of the structure and dynamics of the Earth’sinterior, because of their potential of high ionic conduction, comparedwiththe other mantle-constituent minerals.A variety of CF-, CT- and CM-type transition metal oxides have beensynthesized at high pressure and high temperature to search for possibleionic conductors and compounds with strongly correlated properties. Asdescribed in section “Post-spinel phases in materials science”, CF-typeLiMn2O4 and NaMn2O4 have been synthesized at 4–6 GPa as high ionicconduction materials for candidates of battery cathode materials. The DFTcalculation showed that CF-type AMn2O4 (A = Li, Na, Mg) compoundshave lowest energy barriers than the CT- and CM-type counterparts. Post-spinel-type NaRu2O4 and NaRh2O4 synthesized at∼6 GPa exhibit metallicconductivity, and furthermore the latter shows high thermoelectric prop-erties. CF-type NaV2O4 synthesized at∼ 6 GPa showed a half-metallicground state and was proposed as a magnetic topological material.All the synthesis studies in the viewpoint ofmaterials sciencehavebeenmade at pressures below ∼6 GPa. Using the advanced multi-anvil high-pressure technology, synthesis of large-mass materials at pressure up to∼25 GPa is currently much easily made than before. Large single-crystalssufficient for structure analysis and physical propertymeasurements can besynthesized in the whole pressure range described above using the large-volumemulti-anvil techniques. The search for novel materials is promisingeven up to ∼50 GPa.The chemical and physical properties of CT-type phases have yet to beexperimentally explored; these phases, which have a different octahedralconfiguration from the CF-type, are anticipated to exhibit strongly corre-lated electronic properties, thereby opening up the possibility of uncoveringnew quantum materials. Also, synthesis studies of novel NAL-type 2/3AB2O4·1/3CB2O4 phases have not yet been made at high pressures, sug-gesting that future studies along this direction are desirable.Novel-structured post-spinel phases, such as those in MgFe2O4 andMgAl2O4 described in section “Post-spinel phases in geochemical andmineralogical interest”, can be explored by applying the advanced multi-anvil technology, suggesting that further new-structured post-spinel phasesand consequently novel chemical and physical properties can be discovered.Future high-pressure researchwill continue to explore the synthesis of novelpost-spinel phases and their potential applications.Received: 29 April 2024; Accepted: 20 August 2024;References1. Ringwood, A. E. Composition and Petrology of the Earth’s Mantle(McGraw-Hill, 1975).2. Decker, B. F. & Kasper, J. S. The structure of calcium ferrite. ActaCryst. 10, 332–337 (1957).3. Giesber, H. G., Pennington, W. T. & Kolis, J. W. Redetermination ofCaMn2O4. Acta Cryst. 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This research was supported in part by the Grants-in-Aid ofthe Scientific Research of the Japan Society for the Promotion of Science(JSPS), nos. 25287145 and 17H02986 to M.A., JP23K19067 to T.I., andJP22H04601 and JP20H05276 to K.Y., and by the MEXT-supported pro-gram for the StrategicResearchFoundation at PrivateUniversities.MANA issupported by World Premier International Research Center Initiative (WPI),MEXT, Japan.Author contributionsM.A. conceived the manuscript. M.A., T.I., and K.Y. equally contributed inwriting the manuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s42004-024-01278-0.Correspondence and requests for materials should be addressed toMasaki Akaogi.Peer review informationCommunications Chemistry thanks Kent J Griffithand theother, anonymous, reviewer(s) for their contribution to thepeer reviewof this work. 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Toview a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2024https://doi.org/10.1038/s42004-024-01278-0 Review articleCommunications Chemistry |           (2024) 7:189 12https://doi.org/10.1038/s42004-024-01278-0http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/commschem Post-spinel-type AB2O4 high-pressure phases in geochemistry and materials science Recent developments in high-pressure and high-�temperature experimental techniques using large-�volume apparatus Crystal structures of post-spinel phases CaFe2O4-, CaTi2O4- and CaMn2O4-type phases NAL-type phase Post-spinel phases in geochemical and mineralogical interest Crystal chemical characteristics of post-spinel phases in terms of cation radii Post-spinel phases in materials science Ionic conduction Strongly correlated properties Conclusions and outlook References Acknowledgements Author contributions Competing interests Additional information